Question

If X is a Poisson random variate with mean 3, then P(|X- 3| < 1) will be:
1. \(\dfrac{9}{2} e^{-3}\)
2. 3e^-3
3. \(\dfrac{e^{-3}}{2}\)
4. \(\left( \dfrac{99}{8} \right) e^{-3}\)

Answer 1

Correct Answer - Option 1 : \(\dfrac{9}{2} e^{-3}\)

Answer: Option 4

Concept: 

Poisson Distribution: 

The Poisson probability distribution gives the probability of a number of events occurring in a fixed interval of time or space if these events happen with a known average rate and independently of the time since the last event.

Notation: 

X ~ P(λ)  //where λ is mean

Formulas:

P(X=x) = \({e^{ - λ }}\frac{{{λ^x}}}{{x!}}\)

Calculation:

 It is given that we need to find P(|X- 3| < 1),

after simplifying we get P( 2 < X < 4 )

So between 2 and 4, only one integer value possible is 3.

we get

 P(|X- 3| < 1) = \(\dfrac{9}{2} e^{-3}\)

Hence Option 1 is the correct answer.